Solve for X in the Equation: 35-45=-5x

Q: Why do I get a positive answer when both sides are negative?

When you divide two negative numbers, the result is always positive! $ \frac{-10}{-5} = +2 $ because the negative signs cancel out.

Q: Should I simplify 35 - 45 first or work with -5x first?

Always simplify arithmetic first! Calculate $ 35 - 45 = -10 $ before dealing with the variable term. This makes the equation much cleaner to solve.

Q: How do I know which side to simplify?

Look for arithmetic operations you can perform immediately. In this case, $ 35 - 45 $ can be calculated right away, but $ -5x $ cannot until you know what x equals.

Q: What if I accidentally divide by positive 5 instead of negative 5?

You'll get $ x = -2 $ instead of $ x = 2 $! Always check your work by substituting back into the original equation to catch sign errors.

Q: Can I move -5x to the left side instead?

Yes! You could write $ 35 - 45 + 5x = 0 $, then $ -10 + 5x = 0 $, and finally $ 5x = 10 $. You'll get the same answer: $ x = 2 $.

Linear Equations with Negative Coefficients

Solve for X:

$35-45=-5x$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 We want to isolate the unknown X

00:06 Let's group terms

00:09 Let's isolate the unknown X, and calculate

00:28 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve for X:

$35-45=-5x$

Step-by-step solution

To solve the given linear equation, perform the following operations:

Step 1: Simplify the left-hand side of the equation.

The original equation is:

$35 - 45 = -5x$

Simplify the left side:

$35 - 45 = -10$

Step 2: Substitute the simplified result back into the equation.

We now have:

$-10 = -5x$

Step 3: Solve for $x$ by dividing both sides by $-5$ .

$\frac{-10}{-5} = x$

$x = 2$

Therefore, the solution to the problem is $x = 2$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Simplification: Always perform arithmetic operations on the left side first
Technique: Divide both sides by coefficient: $\frac{-10}{-5} = 2$
Check: Substitute back: $35 - 45 = -5(2) = -10$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to simplify the left side before solving
Don't jump straight to dividing by -5 without calculating 35 - 45 first = confusion and wrong setup! This leads to working with the wrong equation entirely. Always simplify arithmetic expressions completely before isolating the variable.

Practice Quiz

Test your knowledge with interactive questions

Solve for X:

$$ 5x=25 $$

FAQ

Everything you need to know about this question

Why do I get a positive answer when both sides are negative?

When you divide two negative numbers, the result is always positive! $\frac{-10}{-5} = +2$ because the negative signs cancel out.

Should I simplify 35 - 45 first or work with -5x first?

Always simplify arithmetic first! Calculate $35 - 45 = -10$ before dealing with the variable term. This makes the equation much cleaner to solve.

How do I know which side to simplify?

Look for arithmetic operations you can perform immediately. In this case, $35 - 45$ can be calculated right away, but $-5x$ cannot until you know what x equals.

What if I accidentally divide by positive 5 instead of negative 5?

You'll get $x = -2$ instead of $x = 2$ ! Always check your work by substituting back into the original equation to catch sign errors.

Can I move -5x to the left side instead?

Yes! You could write $35 - 45 + 5x = 0$ , then $-10 + 5x = 0$ , and finally $5x = 10$ . You'll get the same answer: $x = 2$ .

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